Fibrations and log-symplectic structures

Abstract

Log-symplectic structures are Poisson structures $\pi$ on $X^{2n}$ for which ${\bigwedge }^n\pi$ vanishes transversally. By viewing them as symplectic forms in a Lie algebroid, the $b$-tangent bundle, we use symplectic techniques to obtain existence results for log-symplectic structures on total spaces of fibration-like maps. More precisely, we introduce the notion of a $b$-hyperfibration and show that they give rise to log-symplectic structures. Moreover, we link log-symplectic structures to achiral Lefschetz fibrations and folded-symplectic structures.

23 pages

References in corpus (1)

• Symplectic and Poisson geometry on b-manifolds

Cited by in corpus (6)

• Coisotropic submanifolds in $b$-symplectic geometry
• Fibrations in semi-toric and generalized complex geometry
• Lagrangian branes with boundary and symplectic methods for stable generalized complex manifolds
• Obstructions for Symplectic Lie Algebroids
• Holomorphic curves in log-symplectic manifolds
• Generalized Luttinger surgery and other cut-and-paste constructions in generalized complex geometry